Stress Concentration around a circular hole on a flat rectangular plate

In summary, the conversation discussed finding the stress concentration around a circular hole in a flat plate under tensile load. The calculation involves using a stress concentration factor, Kt, which can be found using an empirical formula from Peterson's Stress Concentration Factors. Kt is dependent on the diameter of the hole and its distance from the plate edge. The conversation also mentioned a simplification for small hole diameters and distances from the edge.
  • #1
aidiot
4
0
Can anyone help with how to find the analytical solution to problem involving finding the stress concentration around a circular hole in a flat plate.

The plate is has tensile load on both sides.
 
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  • #2
That's a classic example that is in any Mechanics of Materials text. Have you done any searching? The calculation, assuming plane stress, is the regular stress due to the tensile load multiplied by a stress concentration factor, Kt. That value ranges up to 3.0 depending on the size of the hole.

Chart 4.1 in Peterson's Stress Concentration Factors gives an empirical formula for the Kt value.
 
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  • #3
For a circular hole, I'd have imagined that Kt would be independent of the radius.
 
  • #4
Kt is dependent on hole diameter and the distance between the hole edge and the plate edge.
 
  • #5
Oh, I'm thinking of the limit where the hole diameter is small compared to the dimensions of the plate, and small compared to the distance from the nearest edge. If I was looking for an analytical solution to the DEs, I'd have started from that simplification.
 
  • #6
thanks for your help guys...

much appreciated
 

What is stress concentration?

Stress concentration is a phenomenon where the stress in a material is significantly higher in a localized area compared to the surrounding areas. This can occur due to the presence of geometric discontinuities, such as holes or notches, in the material.

How does stress concentration occur around a circular hole on a flat rectangular plate?

When a circular hole is present on a flat rectangular plate, the stress in the material is concentrated around the edges of the hole. This is because the stress is forced to flow around the hole, causing it to increase in magnitude at the edges.

What factors affect the level of stress concentration around a circular hole on a flat rectangular plate?

The level of stress concentration around a circular hole on a flat rectangular plate is affected by the size and shape of the hole, the dimensions and thickness of the plate, and the material properties of the plate. Additionally, the loading conditions and the presence of any other geometric discontinuities can also impact the level of stress concentration.

How does stress concentration impact the strength of a material?

Stress concentration can significantly reduce the strength of a material, as it causes localized areas of high stress which can lead to cracks and failure. It is important to consider stress concentration when designing structures or components to ensure their strength and durability.

How can stress concentration around a circular hole on a flat rectangular plate be reduced?

To reduce stress concentration around a circular hole on a flat rectangular plate, the hole can be smoothed or rounded to distribute the stress more evenly. Additionally, increasing the thickness of the plate or using materials with higher strength can also help reduce stress concentration. Proper design and structural analysis techniques can also help minimize stress concentration.

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